Asked for more details, Amazon provided Recode with the following
explanation:

Echo woke up due to a word in background conversation sounding
like “Alexa.” Then, the subsequent conversation was heard as a
“send message” request. At which point, Alexa said out loud “To
whom?” At which point, the background conversation was
interpreted as a name in the customers contact list. Alexa then
asked out loud, “[contact name], right?” Alexa then interpreted
background conversation as “right”. As unlikely as this string
of events is, we are evaluating options to make this case even
less likely.”

I mean, that all does sound pretty unlikely. But the fact that
Alexa can interpret background conversation as a confirmation is a
big problem.

Unlikely though it sounds, this does seem like the most likely scenario.

I do have a few Echo devices, but I never granted them access to my contacts and never enabled “Calling and Messaging”. If you did, and now wish to disable it, you need to call Amazon on the phone. Not joking.